Given the graph of the following function, determine the intervals on which $f\left(x\right)$  is decreasing.

• A. $(-\infty ,-2)$
• B. $(-2,1)$
• C. $(-2,-\infty )$
• D. $(1,-\infty )$

Answer: (B)

Verified step by step guidance

1. Observe the graph of the function f(x) to identify the intervals where the function is decreasing. A function is decreasing on an interval if, as you move from left to right, the function values are getting smaller.
2. Look for sections of the graph where the slope of the tangent line is negative. This indicates that the function is decreasing in that interval.
3. From the graph, identify the interval from x = -2 to x = 1 where the graph is moving downwards as you move from left to right.
4. Note that the function is not decreasing for x < -2 or x > 1, as the graph is either increasing or constant in those regions.
5. Conclude that the interval where the function f(x) is decreasing is (-2, 1).